Powers of the Vandermonde determinant, Schur Functions, and recursive formulas

Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, we give recursive formulas for the coefficient of the Schur function s_{\m} in the decomposition of an even power of the Vandermonde determinant in $n + 1$ variables in terms of the coefficient of the Schur function s_{\l} in the decomposition of the same even power of the Vandermonde determinant in $n$ variables if the Young diagram of \m is obtained from the Young diagram of \l by adding a tetris type shape to the top or to the left. An extended abstract containing the statement of the results presented here appeared in the Proceedings of FPSAC11Comment: 23 pages; extended abstract appeared in the Proceedings of FPSAC1

AID Overlapping and Polη Hotspots Are Key Features of Evolutionary Variation Within the Human Antibody Heavy Chain (IGHV) Genes

© Copyright © 2020 Tang, Bagnara, Chiorazzi, Scharff and MacCarthy. Somatic hypermutation (SHM) of the immunoglobulin variable (IgV) loci is a key process in antibody affinity maturation. The enzyme activation-induced deaminase (AID), initiates SHM by creating C → U mismatches on single-stranded DNA (ssDNA). AID has preferential hotspot motif targets in the context of WRC/GYW (W = A/T, R = A/G, Y = C/T) and particularly at WGCW overlapping hotspots where hotspots appear opposite each other on both strands. Subsequent recruitment of the low-fidelity DNA repair enzyme, Polymerase eta (Polη), during mismatch repair, creates additional mutations at WA/TW sites. Although there are more than 50 functional immunoglobulin heavy chain variable (IGHV) segments in humans, the fundamental differences between these genes and their ability to respond to all possible foreign antigens is still poorly understood. To better understand this, we generated profiles of WGCW hotspots in each of the human IGHV genes and found the expected high frequency in complementarity determining regions (CDRs) that encode the antigen binding sites but also an unexpectedly high frequency of WGCW in certain framework (FW) sub-regions. Principal Components Analysis (PCA) of these overlapping AID hotspot profiles revealed that one major difference between IGHV families is the presence or absence of WGCW in a sub-region of FW3 sometimes referred to as “CDR4.” Further differences between members of each family (e.g., IGHV1) are primarily determined by their WGCW densities in CDR1. We previously suggested that the co-localization of AID overlapping and Polη hotspots was associated with high mutability of certain IGHV sub-regions, such as the CDRs. To evaluate the importance of this feature, we extended the WGCW profiles, combining them with local densities of Polη (WA) hotspots, thus describing the co-localization of both types of hotspots across all IGHV genes. We also verified that co-localization is associated with higher mutability. PCA of the co-localization profiles showed CDR1 and CDR2 as being the main contributors to variance among IGHV genes, consistent with the importance of these sub-regions in antigen binding. Our results suggest that AID overlapping (WGCW) hotspots alone or in conjunction with Polη (WA/TW) hotspots are key features of evolutionary variation between IGHV genes

Effect of Hadron Dynamics on the Proton Lifetime

A detailed, quantitative re-examination of the effect of hadron dynamics on baryon decay, modeled in terms of Skyrme-field tunneling, indicates that any hadronic suppression should be quite mild. This appears to be another illustration of the `Cheshire-cat' phenomenon, that variation of the apportionment between description of the nucleon as a bag of quarks and description as a Skyrme field configuration has little influence on many nucleon properties. Perhaps the largest remaining uncertainty in evaluating the decay rate has to do with the overlap between a specified quark-antiquark configuration and a final meson state.Comment: minor corrections, 19 pages, 9 figure

Reformulating the Schrodinger equation as a Shabat-Zakharov system

We reformulate the second-order Schrodinger equation as a set of two coupled first order differential equations, a so-called "Shabat-Zakharov system", (sometimes called a "Zakharov-Shabat" system). There is considerable flexibility in this approach, and we emphasise the utility of introducing an "auxiliary condition" or "gauge condition" that is used to cut down the degrees of freedom. Using this formalism, we derive the explicit (but formal) general solution to the Schrodinger equation. The general solution depends on three arbitrarily chosen functions, and a path-ordered exponential matrix. If one considers path ordering to be an "elementary" process, then this represents complete quadrature, albeit formal, of the second-order linear ODE.Comment: 18 pages, plain LaTe

Ferredoxin C2 is required for chlorophyll biosynthesis and accumulation of photosynthetic antennae in Arabidopsis

Ferredoxins (Fd) are small iron-sulphur proteins, with sub-types that have evolved for specific redox functions. Ferredoxin C2 (FdC2) proteins are essential Fd homologues conserved in all photosynthetic organisms and a number of different FdC2 functions have been proposed in angiosperms. Here we use RNAi silencing in Arabidopsis thaliana to generate a viable fdC2 mutant line with near-depleted FdC2 protein levels. Mutant leaves have ~50% less chlorophyll a and b, and chloroplasts have poorly developed thylakoid membrane structure. Transcriptomics indicates upregulation of genes involved in stress responses. Although fdC2 antisense plants show increased damage at photosystem II (PSII) when exposed to high light, PSII recovers at the same rate as wild type in the dark. This contradicts literature proposing that FdC2 regulates translation of the D1 subunit of PSII, by binding to psbA transcript. Measurement of chlorophyll biosynthesis intermediates revealed a build-up of Mg-protoporphyrin IX, the substrate of the aerobic cyclase. We localise FdC2 to the inner chloroplast envelope and show that the FdC2 RNAi line has a disproportionately lower protein abundance of antennae proteins, which are nuclear-encoded and must be refolded at the envelope after import

Effective theory for deformed nuclei

Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu-Goldstone rotational modes and high-energy vibrational and nucleonic degrees of freedom. A power counting is established and the Hamiltonian is constructed at next-to-leading order

Predicting the public health benefit of vaccinating cattle against Escherichia coli O157

Identifying the major sources of risk in disease transmission is key to designing effective controls. However, understanding of transmission dynamics across species boundaries is typically poor, making the design and evaluation of controls particularly challenging for zoonotic pathogens. One such global pathogen is Escherichia coli O157, which causes a serious and sometimes fatal gastrointestinal illness. Cattle are the main reservoir for E. coli O157, and vaccines for cattle now exist. However, adoption of vaccines is being delayed by conflicting responsibilities of veterinary and public health agencies, economic drivers, and because clinical trials cannot easily test interventions across species boundaries, lack of information on the public health benefits. Here, we examine transmission risk across the cattle–human species boundary and show three key results. First, supershedding of the pathogen by cattle is associated with the genetic marker stx2. Second, by quantifying the link between shedding density in cattle and human risk, we show that only the relatively rare supershedding events contribute significantly to human risk. Third, we show that this finding has profound consequences for the public health benefits of the cattle vaccine. A naïve evaluation based on efficacy in cattle would suggest a 50% reduction in risk; however, because the vaccine targets the major source of human risk, we predict a reduction in human cases of nearly 85%. By accounting for nonlinearities in transmission across the human–animal interface, we show that adoption of these vaccines by the livestock industry could prevent substantial numbers of human E. coli O157 cases

A compact statistical model of the song syntax in Bengalese finch

Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in a Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are repeatedly revisited, and allows associations of more than one state to the same syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC, and suggests that adaptation and many-to-one mapping from neural substrates to syllables are important features of the neural control of complex song syntax